Tag Archives: angular momentum

Simulate, Test, Analyze: A Framework For Rigor

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“Have Fun Storming The Castle!”

At the end of this fall semester, the second year students in the Academy rolled and carried their medieval mechanisms of mayhem to the SRHS track and we spent the afternoon watching the devices hurl lacrosse balls across the athletic field.This project was the final performance assessment of the semester and required that students design a gravitationally powered projectile launcher. This is an age old engineering/applied physics project.

Like many engineering projects done in high school, the physics principles governing the dynamics of the project are quite complicated, and ultimately the actual “application” of the science principles is often cursory. Students don’t have the background or mathematical abilities to to do the complex calculations needed to make an optimization adjustment to their mechanical device.This leads to the disconnection between the science content and engineering practice. Students don’t have the ability to make an informed decision about design choices. This is because it is difficult, very difficult.

Over the past few years I have been very interested in addressing this problem. This post discusses a framework that I have been working on to incorporate science into engineering projects. I think this framework allows high school students to engage in difficult scientific analysis without overwhelming them.

A Framework For Rigor

I won’t claim that this is a perfect solution, but so far I think we have experienced some success in creating a tighter relationship between science and engineering.  Last December I helped conduct a workshop at the NCCPA Professional Development Conference in Petaluma, CA. The name of the workshop was “NGSS, Prediction Reports and Your Science Class” and the point of this workshop was to give the attendees a framework for incorporating the Engineering standards into the science curriculum.  My co-presenter (Vipul Gupta) and I focused on the creation of prediction reports using computer simulations as a way to address two very important standards in the NGSS framework:

Using Simulations with Informed Input

Computer simulations are very popular in the educational space. They give teachers and students a virtual space where students can interact with virtual lab equipment or virtual objects that behave similarly to physical objects in the real world. With that said, they can fail to address students misconceptions because they do not always succeed in linking a conceptual model to the physical behavior. I also believe that the best simulations are ones that output data that can be analyzed with other scientific/mathematical tools. I also think that a good simulation requires that students provide meaningful input that gives them opportunities for analyzing the relationship between the input and the output.

Simulations used in engineering projects can be extremely helpful in addressing one of the main problems in engineering education. Students often design and build mechanical devices without understanding the physical principles that govern the design. The design process becomes an exercise in trial and error, or simply is reduced to copying a design from the internet.

To do a predictive analysis of a rocket’s flight, or a bridge’s structural performance is extremely difficult and often requires advanced mathematics and physics. Simulations can give the students the ability to analyze their designs and understand how changing the design inputs affects the output. Once again, it is important to find a simulation that requires students to understand the inputs and outputs.

Virtual Trebuchet

For example, in our project, students were introduced to an online Trebuchet simulation tool. This simulation tool is great because it requires that the student learn how to measure and calculate certain inputs. The students must have a working knowledge of rotational inertia, center of mass, and other concepts before they use the simulation. This was ideal for our project because it gave students a relevance and motivation . They had learn about these concepts in order to actually use the simulation. The students could then change certain inputs and see how that would change the efficiency of the design, or the range of the projectile. The point is that they needed physics knowledge in order to use the tool. They might not have the ability to know how the simulation eventually calculated the output, but they knew that the simulation required an understanding of the inputs.

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Example Report

The Prediction Report

The next step is to ask the students to prepare a prediction report. This report is designed to get students to demonstrate their understanding of the inputs, display evidence of the required calculations or measurements needed to create the inputs and then analyze the simulation outputs. In the report for this project, I asked students to show a set of calculations and measurements for determining the center of mass of their throwing arm and the rotational inertia (moment of inertia). Students also had to provide similar information for the counterweight.  The students then had to run the simulation and document the outputs from the simulation.

The Test:  Data is Needed

The next step is to test the device. To make this step more rigorous and to be able to relate the scientific analytical process to the engineering process, it is crucial for the students to collect data that can be used to analyze the performance of their device/product and then reflect on how they would improve their design.

For this project, we decided to use high-speed video and Vernier’s LoggerPro video analysis software to plot the position of the projectile as it was launched from the device.

The Analysis

The analysis is actually broken into two parts. The first part requires a collection of calculations while the second part uses those calculations to make some qualitative assessments.

For example, in the above project, students had to use the collected position data from the video analysis tool to calculate the kinetic energy of the projectile and then the efficiency of the device. They had to be proficient at the analytical tool, which in itself requires physics content knowledge, providing once again an opportunity to apply scientific models in the analysis portion of this engineering project.

I have included the instructions for the analysis report here: Projectile Launcher Analysis Report.

Finally, students are given the opportunity to use the information gathered in the analysis report to reflect on their design, and more importantly use the information to inform how they would improve on a future design. I have included below the set of questions that I asked my students:

  1. Compare the efficiency calculation of the simulation to the efficiency rating that you calculated for your actual performance. Please describe why you think these values are not the same.
  2. Consider the design of your trigger. What design and fabrication decisions would you change in order to improve your trigger, AND explain WHY you would make those changes.
  3.  Consider the design of your sling. What design and fabrication decisions would you change in order to improve your sling, AND explain WHY you would make those changes.
  4. Consider the design of your release mechanism (called the nose). What design and fabrication decisions would you change in order to improve this mechanism, AND explain WHY you would make those changes.
  5. Consider the design of your arm. What design and fabrication decisions would you change in order to improve your arm, AND explain WHY you would make those changes.
  6. Consider the design of all other components and the overall design. What design and fabrication decisions would you change in order to improve your device (other than the trigger, sling and arm), AND explain WHY you would make those changes.

Conclusion

The overall design of this framework can be boiled down to this:

  • Engage students in a computer simulation that simplifies the process of modeling and analyzing a complex physical/chemical/biological process, but be sure that the simulation requires some conceptual and computational thinking.
  • When testing the performance of the design (bridge, rocket, etc.) make sure that the students are required to  collect data that can be analyzed and that once again demands that they apply their theoretical models.
  • Design an assessment that uses the analysis and gives the students an opportunity to make informed judgements of their designs for the purpose of redesign.

Building The Net Torque Model – Part 3

Appending The Conservative Models

After investigating the causal relationship between torque and angular acceleration, I introduced the possibility to the class that perhaps we also needed to revisit the Energy Transfer Model and the Momentum Transfer Model. The students agreed that an object that is rotating must have energy. This was pretty easy to demonstrate.

I set up a situation in the class where two of the variable inertia disks that we created on the 3D printers were placed at the top of an inclined ramp. The internal marbles were placed at two different configurations inside the disks and then the students predicted which disk would reach the end of the ramp first. I was pleased to find out that the class appeared to agree that the disk with the marbles located closer to the radius would be the winner. I really think that our investigation with the variable inertia disks solidified the students’ conceptual understanding of rotational inertia and the importance of mass distribution.

I have not yet found a good experiment where students could discover the rotational kinetic energy relationship, so I decided to take them through a derivation based on linear kinetic energy. I then asked the students to do some whiteboard work. I asked them to demonstrate that the disks would indeed reach the end of the ramp at different times. Although this wasn’t strictly a constructivist approach, it was good practice in doing some fairly difficult algebra without numerical values – something the students traditionally are not very good at.

We then moved onto momentum. Again, I started by reviewing the Momentum Transfer Model for a particle. At this point the pattern had been fairly well established. The relationship between angular and linear quantities seemed to have taken hold because the students were quick to propose a mathematical definition for angular momentum. Our next goal was to figure out whether this was a conserved quantity.

Mr Holt and I had created a set of metal disks that could be attached to the rotary sensors. I decided to create our own, rather than (sorry Vernier) buy them as I thought that the commercial kit was over priced. It wasn’t too hard to create the disks, especially when you have access to a CNC plasma cutter!

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The students attached one disk to the rotary motion sensor and then got that disk spinning. They then took a second disk that had small magnets attached to it, and dropped this disk onto the spinning disk. The students compared the angular velocity before and after the disks were combined and then calculated the angular momentum of the system before and after. The data we got was quite good with the class getting in the range of only about a 5% to 6% difference.

Wrapping it Up (or Un-Rolling It Down)

As a final deployment, I decided to try the deployment activity that Frank Nochese did with his students. It seemed like a good (and fun) way to wrap up our model (or as I have already argued – models).

Before doing the deployment activity, I reviewed all the model specifics with the students. My point here was to impress on them that what we had not really built a new model, but rather had extended many of the prior particle models to include rigid extended bodies. This generally only required that we consider the moment arm in all the particle models. I think this really helped a number of students see the connection between models that they felt they understood and all this rotational stuff that seemed a bit confusing.

I then set them up with the deployment activity, but I asked them to specifically solve the problem using both energy and net torque. There was some success, but I realized that the task was a bit much for the class. Once again, it is clear that I need to give them more practice with these problems that require multiple steps and that involve algebraic manipulation of symbols without numbers. Plenty of time to practice that!